Selecting items in Outliner using hotkey (B)?
Ctrl + P for parenting only works in the 3D view As far as I know, not in the outliner, so pressing Ctrl + P in the outliner will not work only directly in the viewport.

There are other ways to do this if you want to do it directly from the outliner though, you could use B for selecting as you already do, then click and drag&amp;drop to parent by clicking on the object's icon to the left and dragging from there over to another object you want to parent the selection to.

Would this work for you?

Edit I was just made aware that it only parents one object at a time though, so it may not suit your needs entirely.